POSITIVE-ENERGY IRREPS OF THE QUANTUM ANTI DE SITTER ALGEBRA

We obtain positive-energy irreducible representations of the q-deforme d anti de Sitter algebra U-q(so(3, 2)) by deformation of the classical ones. When the deformation parameter q is N-th root of unity, all the se irreducible representations become unitary and finite-dimensional. Generically, their dimensions are smaller than those of the correspond ing finite-dimensional non-unitary representations of so(3, 2). We dis cuss in detail the singleton representations, i.e. the Di and Rac. Whe n N is odd, the Di has dimension 1/2 (N-2 - 1) and the Rac has dimensi on 1/2 (N-2 + 1) while if N is even, both the Di and Rac have dimensio n 1/2 N-2. These dimensions are classical only for N = 3 when the Di a nd Rac are deformations of the two fundamental non-unitary representat ions of so(3, 2).